sigmoid {biogeom}

Sigmoid Growth Equation

Description

sigmoid is used to calculate the y values (e.g., biomass, height, body length, and so on) at given investigation times.

Usage

sigmoid(expr, P, x, simpver = 1, subdivisions = 100L,
        rel.tol = .Machine$double.eps^0.25, 
        abs.tol = rel.tol, stop.on.error = TRUE, 
        keep.xy = FALSE, aux = NULL)

Arguments

expr

a performance equation or one of its simplified versions.

P

the parameters of the performance equation or one of its simplified versions.

x

the given investigation times.

simpver

an optional argument to use the simplfied version of the performance equation.

subdivisions

please see the arguments for the integrate function in package stats.

rel.tol

please see the arguments for the integrate function in package stats.

abs.tol

please see the arguments for the integrate function in package stats.

stop.on.error

please see the arguments for the integrate function in package stats.

keep.xy

please see the arguments for the integrate function in package stats.

aux

please see the arguments for the integrate function in package stats.

Details

The performance equations denote MbetaE, MBriereE, MLRFE, and their simplified versions. The arguments of P and simpver should correspond to expr (i.e., MbetaE, MBriereE, MLRFE, and MPerformanceE). The sigmoid curve is the integral of the performance equation or one of its simplified versions.

Value

The y values (i.e., biomass, height, body length, and so on) at given investigation times. The growth euqation is actually an integral of the performance equation or one of its simplified versions.

Note

Here, the user can define other performance equations, but new equations or their simplified versions should include the lower and upper thresholds in the x-axis corresponding to y = 0, whose indices of the parameters in P should be the same as those in MbetaE, MBriereE, MLRFE, and MPerformanceE).

Author(s)

Peijian Shi [e-mail], Johan Gielis [e-mail], Brady K. Quinn [e-mail].

References

Jin, J., Quinn, B.K., Shi, P. (2022) The modified Brière equation and its applications. Plants 11, 1769. doi:10.3390/plants11131769

Lian, M., Shi, P., Zhang, L., Yao, W., Gielis, J., Niklas, K.J. (2023) A generalized performance equation and its application in measuring the Gini index of leaf size inequality. Trees - Structure and Function 37, 1555-1565. doi:10.1007/s00468-023-02448-8

Shi, P., Fan, M., Ratkowsky, D.A., Huang, J., Wu, H., Chen, L., Fang, S., Zhang, C. (2017) Comparison of two ontogenetic growth equations for animals and plants. Ecological Modelling 349, 1-10. doi:10.1016/j.ecolmodel.2017.01.012

Shi, P., Gielis, J., Quinn, B.K., Niklas, K.J., Ratkowsky, D.A., Schrader, J., Ruan, H., Wang, L., Niinemets, Ü. (2022) 'biogeom': An R package for simulating and fitting natural shapes. Annals of the New York Academy of Sciences 1516, 123-134. doi:10.1111/nyas.14862

See Also

fitsigmoid, MbetaE, MBriereE, MLRFE, and MPerformanceE

Examples

Pa1 <- c(3, 3, 10, 1)
xv1 <- seq(-5, 15, len=2000)
yv1 <- sigmoid(MBriereE, P=Pa1, x=xv1, simpver=1)
Pa2 <- c(3, 3, 2, 12, 1)
yv2 <- sigmoid(MBriereE, P=Pa2, x=xv1, simpver=NULL)
Pa3 <- c(200, 1.32, 0.85, 12, 3.7, 17)
yv3 <- sigmoid(MPerformanceE, P=Pa3, x=xv1, simpver=1)

dev.new()
plot( xv1, yv2, cex.lab=1.5, cex.axis=1.5, type="l", col=4,
      xlab=expression(italic(x)), ylab=expression(italic(y)) )
lines( xv1, yv1, col=2 )
lines( xv1, yv3, col=3 )

graphics.off()